Non-Hermitian physics has been a newly emerging research front in many branches of physics, like quantum systems, photonics and ultracold atoms. Considering the energy exchange to the environment, the non-Hermitian system can exhibit many intriguing states that have no Hermitian counterparts. Besides, the topological state of matter is another hot topic to many researchers. Topological insulators can be metallic at the surface while keep isolated in the interior. This intriguing property is robust to backscattering and many external disorders, under the topological protection. After being introduced to the field of condensed matter physics to explain the integer quantum hall effect, topological physics has been extended to classical physics rapidly. By combining the non-Hermiticity and topology, the non-Hermitian topological insulator has its unique properties and gives rise to many novel phenomena that can hardly be realized in purely non-Hermitian or topological systems. Owing to the large macroscopic dimension and flexible fabrication, acoustic systems can be regarded as an ideal platform to study the interaction between the non-Hermiticity and topology. The information of the fields, i.e., energy distribution, phase response and frequency response, can be easily detected in many approaches. Also, the gain effect can be mimicked by flow sound interactions, electric acoustic conversion and thermoacoustic effects in acoustics. In this paper, we mainly focused on three aspects of non-Hermitian topological acoustics. First, we introduce the cases that on-Hermitian modulation is imposed on the topological system. Under this circumstance, the degenerated topological states will be divided into two groups. One is related to the amplified mode, the other one is related to the attenuated mode. Second, we introduce the cases that the topological phases are induced by non-Hermiticity solely. Non-Hermiticity can play the role of coupling that changes the real part of eigen-spectra. Thus, with the appropriate non-Hermitian modulation, the acoustic system can be changed from trivial phases into non-trivial phases, associated with the rich topological states. Finally, we introduce the non-Hermitian skin effect, which is a unique feature of non-Hermitian systems. By constructing non-reciprocal couplings or introducing gain and loss modulations to the on-site potential, the conventional bulk-boundary-correspondence breaks and all the bulk modes will be driven to the boundaries of the system. The band structure obtained from periodical boundary conditions is not consistent with that obtained from open boundary conditions, which finally indicates a "point gap" in the complex eigen-spectra. In acoustics, we can utilize the technique of signal processing to realize the non-reciprocal coupling in an active way. Also, we can employ the coupled ring structure to decouple the clockwise and counterclockwise modes to construct pseudo-spin degree. By introducing asymmetric non-Hermitian modulation to the linking ring, the reciprocity can be broken effectively for the modes with specific pseudo-spin degree. Throughout this paper, we have discussed the methods that introduce the non-Hermitian modulation during the simulations and calculations, the versatile approaches to demonstrate the characteristics of non-Hermitian topological phases and the experimental skills in fabrications and measurements. We hope this paper can be useful to the readers who are interested in non-Hermitian topological acoustics.
